To find the simple interest for a loan, we use the formula:
[tex]\[ I = P \cdot r \cdot t \][/tex]
where:
- [tex]\( I \)[/tex] is the interest,
- [tex]\( P \)[/tex] is the principal amount (initial loan),
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( t \)[/tex] is the time in years.
Given:
- The principal ([tex]\( P \)[/tex]) is \[tex]$920.
- The annual interest rate (\( r \)) is 7%.
- The time (\( t \)) is 9 months.
### Step-by-Step Solution:
1. Convert the annual interest rate from a percentage to a decimal:
\[ r = \frac{7}{100} = 0.07 \]
2. Convert the number of months to years:
The given time period is 9 months. Since there are 12 months in a year, we convert months to years by dividing by 12:
\[ t = \frac{9}{12} = 0.75 \, \text{years} \]
3. Plug the values into the simple interest formula:
\[ I = P \cdot r \cdot t \]
\[ I = 920 \cdot 0.07 \cdot 0.75 \]
4. Calculate the interest:
\[ I = 920 \cdot 0.07 \cdot 0.75 = 48.3 \]
### Conclusion:
The simple interest for a loan of \$[/tex]920 at an annual interest rate of 7% for 9 months is:
[tex]\[ \boxed{48.3} \][/tex]
### Summary of Values:
- Principal ([tex]\( P \)[/tex]): \[tex]$920
- Annual Interest Rate (\( r \)): 0.07
- Time in Years (\( t \)): 0.75
- Simple Interest (\( I \)): \$[/tex]48.3
